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The explainable AI (XAI) research community has proposed numerous technical methods, yet deploying explainability as systems remains challenging: Interactive explanation systems require both suitable algorithms and system capabilities that…
Large language models (LLMs) often struggle to objectively identify latent characteristics in large datasets due to their reliance on pre-trained knowledge rather than actual data patterns. To address this data grounding issue, we propose…
A number of flexible tactic-based logical frameworks are nowadays available that can implement a wide range of mathematical theories using a common higher-order metalanguage. Used as proof assistants, one of the advantages of such powerful…
Automated proof generation for formal software verification remains largely unresolved despite advances in large language models (LLMs). While LLMs perform well in NLP, vision, and code generation, formal verification still requires…
Internet browsers use security protocols to protect sensitive messages. An inductive analysis of TLS (a descendant of SSL 3.0) has been performed using the theorem prover Isabelle. Proofs are based on higher-order logic and make no…
Theorem proving is a fundamental task in mathematics. With the advent of large language models (LLMs) and interactive theorem provers (ITPs) like Lean, there has been growing interest in integrating LLMs and ITPs to automate theorem…
This paper investigates demonstration selection strategies for predicting a user's next point-of-interest (POI) using large language models (LLMs), aiming to accurately forecast a user's subsequent location based on historical check-in…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on…
Formally verifying properties of software code has been a highly desirable task, especially with the emergence of LLM-generated code. In the same vein, they provide an interesting avenue for the exploration of formal verification and…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
Large Language Models (LLMs) often do not perform well on queries that require the aggregation of information across texts. To better evaluate this setting and facilitate modeling efforts, we introduce TACT - Text And Calculations through…
Large Language Models (LLMs) can justify or critique their predictions through discussions with other models or humans, thereby enriching their intrinsic understanding of instances. While proactive discussions in the inference phase have…
As artificial intelligence (AI) gains greater adoption in a wide variety of applications, it has immense potential to contribute to mathematical discovery, by guiding conjecture generation, constructing counterexamples, assisting in…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
Large Language Models (LLMs) have displayed astonishing abilities in various tasks, especially in text generation, classification, question answering, etc. However, the reasoning ability of LLMs still faces many debates. The inherent…
Neural theorem proving combines large language models (LLMs) with proof assistants such as Lean, where the correctness of formal proofs can be rigorously verified, leaving no room for hallucination. With existing neural theorem provers…
Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…
Formal methods is pivotal for verifying the reliability of critical systems through rigorous mathematical proofs. However, its adoption is hindered by labor-intensive manual proofs and the expertise required to use theorem provers. Recent…
Large language models (LLMs) show remarkable potential in scientific hypothesis discovery. However, existing approaches face two critical limitations: they treat divergent exploratory ideation and convergent fine-grained refinement as…